MathDB

29

Part of 2014 National Olympiad First Round

Problems(1)

P29 [Geometry] - Turkish NMO 1st Round - 2014

Source:

5/26/2014
Let ABCABC be a triangle such that ∣AB∣=13,∣BC∣=12|AB|=13 , |BC|=12 and ∣CA∣=5|CA|=5. Let the angle bisectors of AA and BB intersect at II and meet the opposing sides at DD and EE, respectively. The line passing through II and the midpoint of [DE][DE] meets [AB][AB] at FF. What is ∣AF∣|AF|?
<spanclass=′latex−bold′>(A)</span> 32<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 52<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 72 <span class='latex-bold'>(A)</span>\ \dfrac{3}{2} \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ \dfrac{5}{2} \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \dfrac{7}{2}
geometryanalytic geometrytrapezoidangle bisector